In valve tappets of the pre-cited type, known, for example, from DE-A 4325610, the soft, unhardened inner element is inserted into the soft, unhardened cup and the peripheral groove is then formed by roller burnishing. Inside the cup, the casing of the inner element and the bead formed by the roller burnished peripheral groove are pressed against each other so that the inner element is firmly connected to the cup. Following this, this partly assembled valve tappet is subjected to a heat treatment whereby the cup and the inner element are hardened. At the end of the heat treatment, the inner element has been somewhat deformed so that, to assure a proper guidance of the hydraulic valve clearance compensation element, machining, particularly grinding work, is required on the inner element. For example, the inner element of the prior art valve tappet comprises a guide sleeve in which the hydraulic valve clearance compensation element is guided for longitudinal displacement. After the common heat treatment of the cup and the inner element, the guide sleeve no longer has a circular cylindrical shape so that the inner wall of the guide sleeve has to be ground.
It is the object of the invention to improve a valve tappet of the generic type so that the machining of the cup after its heat treatment can be dispensed with.